Abelian variety isogeny class 2.193.abw_bkq over $\F_{193}$

• Label: 2.193.abw_bkq
• Base field: $\F_{193}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{193}$
Dimension:	$2$
L-polynomial:	$1 - 48 x + 952 x^{2} - 9264 x^{3} + 37249 x^{4}$
Frobenius angles:	$\pm0.0675123601384$, $\pm0.230069799779$
Angle rank:	$2$ (numerical)
Number field:	4.0.2054400.4
Galois group:	$D_{4}$
Jacobians:	$60$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

$p$-rank:	$2$
Slopes:	$[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28890$	$1372679460$	$51673224895290$	$1925154747813891600$	$71709016301977158272250$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$146$	$36850$	$7187762$	$1387510918$	$267785600306$	$51682541600050$	$9974730240873362$	$1925122950833556478$	$371548729888542460946$	$71708904873245099619250$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 60 curves (of which all are hyperelliptic):

• $y^2=165 x^6+131 x^5+171 x^4+106 x^3+115 x^2+169 x+30$
• $y^2=69 x^6+78 x^5+190 x^4+148 x^3+167 x^2+152 x$
• $y^2=70 x^6+61 x^5+11 x^4+125 x^3+50 x^2+109 x+141$
• $y^2=191 x^6+38 x^5+145 x^4+166 x^3+60 x^2+169 x+11$
• $y^2=154 x^6+43 x^5+35 x^4+5 x^3+131 x^2+87 x+144$
• $y^2=106 x^6+51 x^5+75 x^4+58 x^3+48 x^2+73 x+47$
• $y^2=153 x^6+178 x^5+80 x^4+56 x^3+67 x^2+177 x+152$
• $y^2=90 x^6+73 x^5+132 x^4+138 x^3+66 x^2+116 x+130$
• $y^2=158 x^6+126 x^5+63 x^4+60 x^3+139 x^2+161 x+145$
• $y^2=74 x^6+64 x^5+153 x^4+187 x^3+102 x^2+122 x+174$
• $y^2=52 x^6+106 x^5+137 x^4+160 x^3+161 x^2+39 x+110$
• $y^2=188 x^6+46 x^5+20 x^4+171 x^3+37 x^2+139 x+30$
• $y^2=47 x^6+170 x^5+143 x^4+33 x^3+133 x^2+31 x+44$
• $y^2=149 x^6+57 x^5+117 x^4+42 x^3+158 x^2+x+38$
• $y^2=147 x^6+59 x^5+25 x^4+80 x^3+178 x^2+53 x+76$
• $y^2=47 x^6+155 x^5+99 x^4+161 x^3+83 x^2+171 x+86$
• $y^2=7 x^6+127 x^5+126 x^4+53 x^3+159 x^2+21 x+26$
• $y^2=64 x^6+181 x^5+179 x^4+51 x^3+180 x^2+89 x+102$
• $y^2=37 x^6+56 x^5+89 x^4+74 x^3+121 x^2+117 x+105$
• $y^2=119 x^6+147 x^5+12 x^4+135 x^3+59 x^2+58 x+123$
• and

• $y^2=121 x^6+66 x^5+170 x^4+85 x^3+21 x^2+103 x+117$
• $y^2=182 x^6+103 x^5+188 x^4+184 x^3+181 x^2+131 x+173$
• $y^2=135 x^6+52 x^5+37 x^4+6 x^3+164 x^2+182 x+164$
• $y^2=120 x^6+6 x^5+92 x^4+39 x^3+130 x^2+87 x+116$
• $y^2=158 x^6+27 x^5+28 x^4+18 x^3+152 x^2+136 x+82$
• $y^2=174 x^6+178 x^5+24 x^4+89 x^3+58 x^2+156 x+73$
• $y^2=154 x^6+154 x^5+84 x^4+48 x^3+164 x^2+33 x+113$
• $y^2=45 x^6+161 x^5+5 x^4+54 x^3+17 x^2+104 x+159$
• $y^2=93 x^6+120 x^5+188 x^4+101 x^3+97 x^2+5 x+36$
• $y^2=163 x^6+91 x^5+56 x^4+39 x^3+156 x^2+113 x+163$
• $y^2=183 x^6+132 x^5+106 x^4+30 x^3+150 x^2+175 x+4$
• $y^2=123 x^6+68 x^5+17 x^4+76 x^3+120 x^2+42 x+186$
• $y^2=167 x^6+169 x^5+146 x^4+30 x^3+41 x^2+162 x+51$
• $y^2=108 x^6+61 x^5+74 x^4+160 x^3+69 x^2+147 x+43$
• $y^2=11 x^6+137 x^5+71 x^4+131 x^3+68 x^2+23 x+4$
• $y^2=124 x^6+145 x^5+129 x^4+27 x^3+141 x^2+66 x+115$
• $y^2=159 x^6+99 x^5+29 x^4+91 x^3+87 x^2+101 x+11$
• $y^2=162 x^6+2 x^5+173 x^4+8 x^3+37 x^2+14 x+179$
• $y^2=178 x^6+59 x^5+151 x^4+118 x^3+76 x^2+104 x+177$
• $y^2=51 x^6+41 x^5+82 x^4+44 x^3+73 x^2+22 x+38$
• $y^2=174 x^6+177 x^5+18 x^4+13 x^3+111 x^2+70 x+122$
• $y^2=38 x^6+173 x^5+48 x^4+128 x^3+98 x^2+160 x+138$
• $y^2=101 x^6+40 x^5+173 x^4+137 x^3+92 x^2+188 x+132$
• $y^2=47 x^6+104 x^5+126 x^4+31 x^3+25 x^2+183 x+140$
• $y^2=104 x^6+103 x^5+8 x^3+191 x^2+164 x+182$
• $y^2=19 x^6+12 x^5+9 x^4+187 x^3+143 x^2+155 x+157$
• $y^2=136 x^6+4 x^5+101 x^4+166 x^3+101 x^2+51 x+175$
• $y^2=20 x^6+79 x^5+131 x^4+114 x^3+150 x^2+151 x+105$
• $y^2=82 x^6+12 x^5+34 x^4+140 x^3+184 x^2+10 x+93$
• $y^2=154 x^6+98 x^5+87 x^4+10 x^3+68 x^2+43 x+110$
• $y^2=111 x^6+104 x^5+132 x^4+133 x^3+192 x^2+124 x+70$
• $y^2=18 x^6+148 x^5+44 x^4+54 x^3+134 x^2+190 x+51$
• $y^2=189 x^6+47 x^5+180 x^4+177 x^3+112 x^2+170 x+185$
• $y^2=166 x^6+94 x^5+42 x^4+32 x^3+91 x^2+126 x+28$
• $y^2=111 x^6+116 x^5+6 x^4+56 x^3+175 x^2+37 x+142$
• $y^2=171 x^6+x^5+76 x^4+105 x^3+76 x^2+100 x+28$
• $y^2=113 x^6+159 x^5+43 x^4+157 x^3+181 x^2+28 x+109$
• $y^2=77 x^6+139 x^5+67 x^4+27 x^3+118 x^2+150 x+159$
• $y^2=147 x^6+134 x^5+11 x^4+66 x^3+145 x^2+95 x+48$
• $y^2=117 x^5+182 x^4+13 x^3+51 x^2+114 x+78$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{193}$.

Endomorphism algebra over $\F_{193}$

The endomorphism algebra of this simple isogeny class is 4.0.2054400.4.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.

Twist	Extension degree	Common base change
2.193.bw_bkq	$2$	(not in LMFDB)